Problem: Multiply. $94 \times 8.12 =~$
$94 \times812$ and $94 \times 8.12$ multiply the same digits in the same order. So, the product of both problems will also have the same digits in the same order. Let's multiply $94\times 812$. Then we can estimate to place the decimal point in the product of $94 \times 8.12$. $\begin{aligned} 812&\\ \underline{ \times 94}&\\ 8}\\ 40}\\ 3{,}200}\\ 180}\\ 900}\\ \underline{+72{,}000}}\\ 76{,}328 \end{aligned}$ Let's estimate to place the decimal in $94 \times8.12$. $\begin{aligned} 94 \times 8.12 &\approx 90\times 8\\\\ &\approx720 \end{aligned}$ Where can we place the decimal in $76{,}328$ to get a product close to $720$ ? $94 \times 8.12 = 763.28$